Journal of Finance and Accounting
ISSN (Print): 2333-8849 ISSN (Online): 2333-8857 Website: Editor-in-chief: Apply for this position
Open Access
Journal Browser
Journal of Finance and Accounting. 2022, 10(1), 1-6
DOI: 10.12691/jfa-10-1-1
Open AccessReview Article

Evolution of the CAPM: From “Premium for Risk” to “Sharp-Linter-Black Model”

Huseyin Yilmaz1,

1Department of Accounting and Finance, Faculty of Economics and Administrative Sciences, Bilecik Şeyh Edebali University, Turkey

Pub. Date: February 07, 2022

Cite this paper:
Huseyin Yilmaz. Evolution of the CAPM: From “Premium for Risk” to “Sharp-Linter-Black Model”. Journal of Finance and Accounting. 2022; 10(1):1-6. doi: 10.12691/jfa-10-1-1


The evolution of the Capital Assets Pricing Model (CAPM) started with the Williams [1] with the formula of “Premium for Risk”. Then, Hicks [2] and Markowitz [3] gave some opinions about risk premium and the value of an individual financial asset, respectively. Then, Treynor [4] and [5] brought some contributions to the model such as risk premium for equity and present price of a share. Sharp [6] added to the model the expected rate of return and he also transferred the standard deviation from statistics to the CAPM evolution. Linther [7] gave another risk premium approach with a different formula. Mossin [8] continued to improve the CAPM with his contributions of expected rate of return on a unit of a risky asset, return of a unit of a riskless asset, and the risk margin formulas. Black [9] completed the CAPM evolution with his model called “Sharp Linther Black Model”.

the CAPM risk premium beta standard deviation variance covariance Williams Hicks Markowitz Sharp Linther Mossin Treynor Black

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit


[1]  Williams, J.B. (1938), The Theory of Investment Value, North Holland Publishing Company, Amsterdam, Netherland.
[2]  Hicks, J.R (1939), Value and Capital, Oxford University Press, Second Edition, Great Britain.
[3]  Markowitz H. (1952), “Portfolio Selecting”, The Journal of Finance, Vol.7, No.1, pp.77-91.
[4]  Treynor J.L. (1961), “Market Value, Time, and Risk”, Unpublished manuscript, “Rough Draft” Dated 8.8.1961, 95-209, pp.1-45.
[5]  Treynor J. L. (1962), “Toward A Theory of Market Value of Risky Assets”, Rough Draft, Revised 12/28/02, with minor edits by Craig William French, pp.1-19.
[6]  Sharp W. (1964), “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk”, The Journal of Finance, Vol. 19, No. 3, pp. 425-442.
[7]  Linther J. (1965a), “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets”, The Review of Economics and Statistics, Vol. 47, No.1, pp.13-37.
[8]  Mossin J. (1966), “Equilibrium in a Capital Asset Market”, Econometrica, Vol. 34, No. 4, pp. 768-783.
[9]  Black F. (1972), “Capital Market Equilibrium with Restricted Borrowing”, The Journal of Business”, Vol.45, No.3, pp.444-455.
[10]  Fama E. and French R. (2004), “The Capital Asset Pricing Model: Theory and Evidence”, Journal of Economic Perspectives, Vol.18, No.3, pp.25-46.
[11]  Linther J. (1965b), “Security Prices, Risk and Maximal Gains From Diversification”, The Journal of Finance, Vol.20, No.4, pp.587-615.